This is a quick sample:
It has a border, a text and two brushes with the stamp effect.
In this state, the brush colour is white and they're above the content. So it conveys the look I want to achieve. Obviously, this won't work if the background isn't white. So what I need is real transparency through form.
You can change the brushes colour and follow my steps to reproduce above.
1) Create the text as live Type and change the Fill Color as desired (just click the Fill box in the Toolbox and set the colour in the Color palette, pick a swatch, or whatever), and the stamp frame if any (circles, whatever), and set the Fill/Stroke Color as desired;
2) Select whichever brush you like, set the Stroke Colour to white, and scribble on top of the Type/frame in 1) so you get the desired appearance;
3) Select everything and in the Appearance palette flyout (upper right arrow) tick Make Opacity Mask with Clip unticked and Invert Mask ticked.
Edit: This was based on the link (to the NU stamp) in the OP; I cannot see any artwork appearing with the link in post #3.
Okay, I found the answer myself. I can assembly multiple objects into one assembled object (how's that called in English? German: "Zusammengesetzter Pfad") and use the pathfinder operations on two of these. That works a lot easier now.
Type needs to be converted to paths, then the whole group can be converted. Multiple brushes also need to be converted to outlines and can be assembled as well. So only two objects remain.